Coherent Phonon‐Induced Gigahertz Optical Birefringence and Its Manipulation in SrTiO3

Abstract Birefringence, which modulates the polarization of electromagnetic wave, has been commercially developed and widely used in modern photonics. Fostered by high‐frequency signal processing and communications, feasible birefringence technologies operating in gigahertz (GHz) range are highly desired. Here, a coherent phonon‐induced GHz optical birefringence and its manipulation in SrTiO3 (STO) crystals are demonsrated. With ultrafast laser pumping, the coherent acoustic phonons with low damping are created in the transducer/STO structures. A series of transducer layers are examined and the optimized one with relatively high photon–phonon conversion efficiency, i.e., semiconducting LaRhO3 film, is obtained. The most intriguing finding here is that, by virtue of high sensitivity to strain perturbation of STO, GHz optical birefringence can be induced by the coherent acoustic phonons and the birefringent amplitudes possess crystal orientation dependence. Optical manipulation of both coherent phonons and its induced GHz birefringence by double pump technique are also realized. These findings reveal an alternative mechanism of ultrafast optical birefringence control, and offer prospects for applications in high‐frequency acoustic‐optics devices.

. Transient reflectivity spectra ∆R of the LRO/STO (110) structure at different pump and probe wavelengths. The bold fonts in the legend represent the pump light wavelength.      An ultrashort optical pump pulse is partially absorbed by a thin LRO transducer layer, and a strain pulse was generated by the instantaneous thermal expansion [1] , which could be regarded as a wave packet arising from the superposition of longitudinal acoustic phonons having different wave vectors [2] . The acoustic pulse travels in the STO layer at the speed of sound v and induces a refractive index modulation, which constitutes a traveling scattering plane inside STO crystal. The schematic sketch is shown in Figure S7(a), the input probe beam (E 1 ) was injected into the LRO/STO heterostructure at an angle of φ to surface normal, and beam 1 and beam 2 were reflected from by the interface and the traveling scattering plane (at the position of z = vt), respectively.
To simulate the polarization dependence of the transient reflectivity oscillations, the interaction between the reflected beam 1 and beam 2 was considered in the numerical simulation. The laser intensity I(P) detected by the photoelectric detector can be considered as follows: Here, δ is the phase difference between beam 1 and beam 2 at the photodetector, E R1 and E R2 are the complex electric field values for the reflected beam 1 and beam 2, respectively. According to the principle of vector decomposition, linearly polarized light can be decomposed into s and p polarized components. Linearly polarized light with the polarization angle θ can be considered as follows: Therefore, equation (1) can be written as: Here, δ s and δ p are phase differences between beam 1 and beam 2 are for the s and p polarized components at the photodetectors, respectively. Based on Fermat's principle, δ s and δ p can be written as: Here, n = 2.34 is the refractive index of STO at 800 nm [3] , v s stands for the value of longitudinal sound velocity (8088 m s -1 ), λ probe represents the probe wavelength in vacuum, t is the delay time and φ is the probe incidence angle (45°). For 110 oriented STO, there is a difference of π between δ s and δ p due to the half-wave loss of s component, Based on this simple model, the TR-ΔR at probe polarization angels of 0° (p-polarization), 45°, and 90° (s-polarization) were numerically simulated, as shown in Figure S7(b). From the simulated results, the amplitudes of the transient reflectivity oscillations are large at 0° and 90°, while the amplitude at 45° is hard to be observed, which are similar to the experimental results in Figure 3(c).
The amplitude of the transient reflectivity oscillations versus the polarization angle of the probe beam was also numerically simulated, as shown in Figure S7(c). The polarization dependence trace has four-fold symmetry with largest values at 0°, 90°, 180° and 270°, consistent with that observed in experiment as shown in Figure 3(b). From the above results, we can conclude that this simple mode can explain the oscillation behavior in the ultrafast reflectivity changes.
At this point, the polarization angle of the probe laser is:    To realize the coherent phonons and optical birefringence manipulation in the LRO/STO structure, time-resolved optical reflectivity (TR-ΔR) measurement with two pump pulses was performed. The experimental setup and detection principle were shown in the schematic in Figure S13. Sample were kept at room temperature. The light source was a Ti:sapphire pulse laser with a wavelength of 800 nm, a repetition rate of 1 kHz, and a pulse duration of 100 fs. A beam splitter was used to divide the laser output into two parts. After converting the pump pulse wavelength to 400 nm with a barium borate crystal (BBO) by second harmonic generation (SHG) process, the pump beam was further divided into two optical beams by another beam splitter. To control the time delay between the pump pulses of the two beams (Δt), a delay stage (DS2) was placed in the one of pump beams. A positive sign of Δt means that the pump pulse of the beam that passed through DS2 (the "second" pump pulse) arrived later at the sample surface than the pump pulse of the other beam (the "first" pump pulse).
The relative delay (t) between the first pump pulse and the probe pulse is scanned by the DS1 delay stage. The incident angle of the probe beam is ~45° with respect to the normal direction of the sample plane, while the pump was ~35° to the surface normal. The beams sizes are the same as the single pump experiment as mentioned above. Both pump 1 and pump 2 fluences are 9.6 mJ cm -2 . The pump beam was chopped at a rate of 635 Hz to measure the relative changes in the reflectance between the pump perturbed (R 0 + ΔR) and unperturbed (R 0 ) samples. A low noise photodetector (New Focus, Model 2007) and a lock-in amplifier (Zurich Instruments, MFLI 500 kHz) are used to improve the signal-to-noise ratio. To track the transient optical birefringence effect Δθ R , the reflected light from the sample was first filtered to remove the pump, passed through a half-wave plate and a Wollaston prism, and then detected by a pair of balanced photodiodes. The pump-induced change in the rotation of the polarization angle was determined as the ratio of the intensity imbalance/the sum intensity of each photodiode obtained from a lock-in amplifier locked at the pump modulation frequency.